双平行圆形隧道稳定的塑性极限分析上限解

从塑性极限分析上限法的基本原理出发，通过分析单圆形隧道4种类型垮落机制所获得的稳定率上限解，构建黏土层中双平行圆形隧道的垮落机制，阐述双平行圆形隧道稳定与垮落间的临界稳定分析过程，导出浅土层中双平行圆形隧道稳定率的上限方程。该方程根据隧道间不同距离，综合两隧道重叠（单隧道）、两隧道相接触、相互影响的双隧道以及互不影响的两单隧道的稳定特征。通过该方程进一步讨论土重对双隧道稳定率上限解的影响。最后，由离心模型试验结果证实其上限解的正确性。

UPPER BOUND SOLUTIONS OF PLASTIC LIMIT ANALYSIS FOR THE STABILITY OF TWO PARALLEL CIRCULAR TUNNELS

According to the principle of the upper bound theorem of plastic limit analysis,through the analysis of the upper bound solutions of stability ratios which are obtained from four collapse mechanisms of a single circular tunnel,a collapse mechanism of two parallel circular tunnels with same diameters in cohesive soil is established.An analysis procedure of critical state of the two parallel circular tunnels between the stability and collapse is described;and an upper bound equation of stability ratio for two parallel circular tunnels with same diameters in cohesive soil is obtained.The equation expresses the stability characteristics of the two tunnels with the different pillar width between them,including two tunnels overlapping(a single tunnel),two tunnels touching,two tunnels influencing each other and two single tunnels.The upper bound solutions of stability ratio under the conditions of weightless soil and soil with self-weight are discussed from the equation.In the end,the correctness of the upper bound solutions is proved by the results of centrifugal model tests.